Unifying strongly clean power series rings
| Autor: | Alexander J. Diesl, Daniel R. Shifflet |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Power series
Pure mathematics Class (set theory) Ring (mathematics) Algebra and Number Theory Mathematics::Commutative Algebra Statement (logic) 010102 general mathematics 010103 numerical & computational mathematics 01 natural sciences New class Condensed Matter::Superconductivity 0101 mathematics Mathematics |
| Zdroj: | Communications in Algebra. 46:4448-4462 |
| ISSN: | 1532-4125 0092-7872 |
| DOI: | 10.1080/00927872.2018.1444174 |
| Popis: | It is unknown whether a power series ring over a strongly clean ring is, itself, always strongly clean. Although a number of authors have shown that the above statement is true in certain special cases, the problem remains open, in general. In this article, we look at a class of strongly clean rings, which we call the optimally clean rings, over which power series are strongly clean. This condition is motivated by work in [10] and [11]. We explore the properties of optimally clean rings and provide many examples, highlighting the role that this new class of rings plays in investigating the question of strongly clean power series. |
| Databáze: | OpenAIRE |
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